New Avalanche Dynamics Model

Fig. 1: Dry powder avalanche at the test site "Vallée de la Sionne"

To dimension buildings in avalanche prone territory it is necessary to predict avalanche velocity, pressure, flow height and runout distance. Switzerland -- and many other countries in the world – have traditionally used a mathematical model for this purpose developed by A. Voellmy after the extreme avalanches winters in Switzerland (1951) and Austria (1955).

Voellmy correctly identified the core problem in avalanche science: the mathematical description of the frictional forces acting on the avalanche. The frictional forces determine how fast the avalanche flows and the runout distance. Voellmy considered snow to be a mixture of fluid and solid parts and therefore proposed a mathematical model consisting of two constant parameters, one parameter describing the solid phase, the other parameter describing the more fluid like behavior of flowing snow. However, Voellmy was very aware the solid frictional part could be reduced by shaking or “vibration”. Although he thought this effect was important, he did not explicitly include in his model. Voellmy’s model was useful in practice, above all for the calculation of extreme avalanches where the values of the two parameters could be determined.

Fig. 2: Fluctuation energy affects the velocity of an avalanche.

The SLF obtained a wealth of avalanche data from the extreme winter of 1999 and the SLF continues to perform full scale tests in Vallée de la Sionne. The analysis of such data revealed that the Voellmy model is useful, but also that it does not explain all the physical phenomena associated with snow avalanches. For example, Voellmy’s model cannot predict the formation of the dangerous powder cloud or how avalanches exactly deposit mass in the runout zone. The model is too simple for this purpose, but this was never the intention of Voellmy.

To remedy this situation, SLF researchers mathematically introduced the idea of “vibrations” into their mathematical models. Avalanches consist of snow granules and ice particles of various shapes and sizes. They are all not moving with the same speed. When these granules flow, collisions and other interactions cause the granules to move in different directions (Fig. 2). The sum of all of these random movements is the fluctuation energy or the “vibration” of Voellmy. The fluctuation energy can vary from the head to tail of the avalanche. For example, at the avalanche front where the powder cloud is formed, usually has higher fluctuation energy than the tail of the avalanche. The new mathematical models explicitly contain equations describing how the fluctuation energy is created and how it is dissipated.  The equation coefficients are a function of the surface roughness and material properties of the flowing snow.  The original Voellmy model is still used, but now the frictional parameters depend on the fluctuation energy.

Fig. 3: RAMMS - a two-dimensional modelling in 3D alpine terrain.

The consequences of this simple modification were unexpected. For example, avalanches of different size could be simulated with the same model parameters. A simple stability analysis of the equations revealed whether an avalanche stops immediately after release, or whether the avalanche continues to flow and grow. However, the major advantage of calculating the fluctuation energy is that the mathematical formulation can be introduced into simulation software like RAMMS (Fig. 3) and therefore might find application one day in practice and research. It is also comforting to know that the Voellmy model, although simple, is not too wrong after all.